Related papers: Arrow-Type Impossibility for Genuinely Modal Judgm…
A well-known conjecture of Orlov asks whether the existence of a full exceptional collection implies rationality of the underlying variety. We prove this conjecture for arithmetic toric varieties over general fields. We also investigate a…
We extend our approach to abstract syntax (with binding constructions) through modules and linearity. First we give a new general definition of arity, yielding the companion notion of signature. Then we obtain a modularity result as…
An inconsistent knowledge base can be abstracted as a set of arguments and a defeat relation among them. There can be more than one consistent way to evaluate such an argumentation graph. Collective argument evaluation is the problem of…
We contemplate a higher-level bipolar abstract argumentation for non-elementary arguments such as: X argues against Ys sincerity with the fact that Y has presented his argument to draw a conclusion C, by omitting other facts which would not…
Properties expressed as the provability of a first-order sentence can be disproved by just finding a model of the negation of the sentence. This fact, however, is meaningful in restricted cases only, depending on the shape of the sentence…
Aggregation functions are widely used in answer set programming for representing and reasoning on knowledge involving sets of objects collectively. Current implementations simplify the structure of programs in order to optimize the overall…
The provability logic of a theory T is the set of modal formulas, which under any arithmetical realization are provable in T . We slightly modify this notion by requiring the arithmetical realizations to come from a specified set $\Gamma$.…
Parametricity is a key metatheoretic property of type systems, which implies strong uniformity & modularity properties of the structure of types within systems possessing it. In recent years, various systems of dependent type theory have…
Motivated by questions like: which spatial structures may be characterized by means of modal logic, what is the logic of space, how to encode in modal logic different geometric relations, topological logic provides a framework for studying…
The collaborative reasoning for understanding each image-question pair is very critical but under-explored for an interpretable Visual Question Answering (VQA) system. Although very recent works also tried the explicit compositional…
We study structural limitations of purely algebraic reasoning in the analysis of arithmetic dynamical systems. Rather than addressing the truth of specific conjectures, we introduce a fragment - relative notion of algebraic refutability for…
Weighted bipolar argumentation frameworks offer a tool for decision support and social media analysis. Arguments are evaluated by an iterative procedure that takes initial weights and attack and support relations into account. Until…
Propositional and modal inclusion logic are formalisms that belong to the family of logics based on team semantics. This article investigates the model checking and validity problems of these logics. We identify complexity bounds for both…
This is a survey on propositional proof complexity aimed at introducing the basics of the field with a particular focus on a method known as feasible interpolation. This method is used to construct "hard theorems" for several proof systems…
Complex reasoning problems are most clearly and easily specified using logical rules, but require recursive rules with aggregation such as count and sum for practical applications. Unfortunately, the meaning of such rules has been a…
Among the various forms of reasoning studied in the context of artificial intelligence, qualitative reasoning makes it possible to infer new knowledge in the context of imprecise, incomplete information without numerical values. In this…
We extend the meet-implication fragment of propositional intuitionistic logic with a meet-preserving modality. We give semantics based on semilattices and a duality result with a suitable notion of descriptive frame. As a consequence we…
An exhaustive survey of categorical propositions is proposed in the present paper, both with respect to their nature and the logical problems raised by them. Through a comparative analysis of Term Logic and First-Order Logic, it is shown…
Pure, or type-free, Linear Logic proof nets are Turing complete once cut-elimination is considered as computation. We introduce modal impredicativity as a new form of impredicativity causing the complexity of cut-elimination to be…
Sequential propositional logic deviates from ordinary propositional logic by taking into account that during the sequential evaluation of a propositional statement,atomic propositions may yield different Boolean values at repeated…